对谱半径至多为$\sqrt[r]{2+\sqrt{5}}$的超图的分类研究

Hypergraphs with Spectral Radius at Most $\sqrt[r]{2+\sqrt{5}}$

中文关键词:  $r$-一致超图  谱半径  $\alpha$-正则

英文关键词:$r$-uniform hypergraphs  spectral radius  $\alpha$-normal

中文摘要:

      在本文,我们研究谱半径至多为$\sqrt[r]{2+\sqrt{5}}$的超图.我们得到此种超图必须具有一个基普结构,这与Woo-Neumaier在2007年对谱半径至多为$\frac{3}{2}\sqrt{2}$的图的分类结果类似.

英文摘要:

      In this paper, we consider the $r$-uniform hypergraphs $H$ with spectral radius at most $\sqrt[r]{2+\sqrt{5}}$. We show that $H$ must have a quipus-structure, which is similar to the graphs with spectral radius at most $\frac{3}{2}\sqrt{2}$ [Woo-Neumaier, Graphs Combin. 2007].